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Question: A black dot used as a full stop at the end of a sentence has a mass of about one attogram. Assuming ...

A black dot used as a full stop at the end of a sentence has a mass of about one attogram. Assuming that the dot is made up of carbon, calculate the approximate number of carbon atoms present in the dot. (1 attogram=10−18g)\left( {1{\text{ attogram}} = {{10}^{ - 18}}{\text{g}}} \right)

Explanation

Solution

To answer this question, you must recall Avogadro's number. The Avogadro’s constant or Avogadro’s number gives the number of molecules/ atoms/ ions present in one mole of a substance. We shall find the moles of carbon present and then multiply it with Avogadro’s number to get the number of atoms.
Formula used:
n=wMn = \dfrac{w}{M}
Where, nn denotes the number of moles of the given substance
ww denotes the given mass of the substance
And, MM denotes the molar mass of the given substance.

Complete step by step answer:
The value of Avogadro’s constant is 6.023×10236.023 \times {10^{23}} and it is represented as NA{N_A}. Thus, 1 mole of any substance contains 6.023×10236.023 \times {10^{23}} particles.
In the question, we are given a dot with a mass of one attogram. The dot is given to be made up of carbon atoms. We know that one attogram weighs about 1018g{10^{18}}g.
First, we find the number of moles of carbon present in the dot. We know that it is given by the formula n=wMn = \dfrac{w}{M}
Substituting the values for carbon atoms, we get, n=10−1812n = \dfrac{{{{10}^{ - 18}}}}{{12}}
The number of atoms in n moles of carbon are given by N=n×NAN = n \times {N_A}
Substituting the values, we get, N=10−1812×6.023×1023N = \dfrac{{{{10}^{ - 18}}}}{{12}} \times 6.023 \times {10^{23}}
⇒N=5.02×104\Rightarrow N = 5.02 \times {10^4}

So the number of atoms of carbon present in a dot of mass one attogram is 5.02×1045.02 \times {10^4}.

Note:
The value of the Avogadro constant is given in such a way so that the mass of one mole of any given chemical substance (in grams) has the same numerical value (for all practical purposes) as the mass of one molecule of the substance in terms of atomic mass units (amu). One atomic mass unit is 1/12th1/12th of the mass of one carbon- 12 atom. It is approximately equal to the mass of one proton or one neutron.